Multiscale mechanical characterization of soft matter

MULTISCALE MECHANICAL CHARACTERIZATION OF SOFT MATTER NICHOLAS AGUNG KURNIAWAN NATIONAL UNIVERSITY OF SINGAPORE 2011 MULTISCALE MECHANICAL CHARACTERIZATION OF SOFT MATTER NICHOLAS AGUNG KURNIAWAN (B.Eng.(Hons.), NUS) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY NATIONAL UNIVERSITY OF SINGAPORE 2011 Acknowledgments The work presented in this thesis is the result of a number of collaborations. It has been an inspiring and wonderful experience to work with these lively scientists. My first word of thanks must go to my supervisor, Prof. Raj Rajagopalan. The influence of his mentoring over my graduate course cannot be overstated. I admire his openness to letting students take responsibility for seeing their ideas through and his willingness to constantly create opportunities for his students. His enthusiasm, clarity of thought, tireless work ethic, and integrity serve as a constant reminder of what it takes to be a great scientist. I am deeply indebted to my co-supervisor, Prof. Lim Chwee Teck, who helped shape the course of my project in the early stages of my research. His passion for interdisciplinary and collaborative research has positively infected how I think and approach science. I am equally grateful to my committee members, Prof. Yan Jie and Prof. Sow Chorng Haur, for their time and consideration. Their inputs and support have helped me through the important milestones of this work. I would also like to thank other scientists that have helped my project in one way or another, especially Prof. Too Heng-Phon and Prof. Johan van der Maarel for the fruitful discussions. I feel fortunate to have worked closely with Sun Wei in the first stage of my work. Having mechanical engineering background like I do, she understood my early difficulties with cell cultures, biochemical protocols, and assays, and her patient guidance definitely made my path easier. Besides her knack for detailed intellectual discussions, her relentless fervor has been instrumental in my development as a i researcher. The simulation work in this thesis is only possible through the help of Søren Enemark. Søren is highly skilled in algorithms and molecular dynamics simulations, and is a prolific yet practical thinker. His ability to methodically dissect the physics behind simulations has helped bring results into focus. More recently, I have had the pleasure to work with Kat Wong on the biological perspectives and applications of this work. Her youthful energy and exuberance, not to mention her flair to visually beautify things, made her really fun to work with. It was a real joy being around these people. I am also thankful to the other members and former members of Prof. Raj’s research group (Vigneshwar Ramakrishnan, Srivatsan Jagannathan, Li Jianguo, Dhawal Shah, Harve Karthik, Sivashankari Gnanasambandam, Reno Antony, Manju Garg, and Adam Bin Idu Jion) and Prof. Lim’s lab (Tan Swee Jin, William Chung, Li Qingsen, Earnest Mendoz, Yuan Jian, Vedula Sri Ram Krishna, Li Ang, Lim Tong Seng, and many others) for creating not only an intellectually stimulating and research-conducive environment, but also a supportive and friendly atmosphere. I would like to acknowledge NUS Graduate School for Integrative Sciences and Engineering (NGS) and the Global Enterprise for Micro-Mechanics and Molecular Medicine (GEM4) for the financial support of my graduate education. In addition, my research efforts have been greatly aided by administrative and logistical supports from the NGS office (Irene Chuan, Rahayu Aziz, Vivien Li, Ivy Wee, and Neo Cheng Bee), ChBE office (Alyssa Tay and Ang Wee Siong), NanoBiomechanics lab (Hairul Nizam), and rheology lab (Jamie Siew). ii Last, I would like to express my greatest gratitude to my family, especially my mother, Ratna Susanti, and my fiancé, I Fon Bambang, for their endless support and love throughout these years. iii Publications Published works: Kurniawan, N. A., Lim, C. T, and Rajagopalan, R. (2010). Image correlation spectroscopy as a tool for microrheology of soft materials. Soft Matter, 6(15), 3499-3505. Kurniawan, N. A. and Rajagopalan, R. (2011). Probe-independent image correlation spectroscopy. Langmuir 27(6), 2775-2782. Submitted manuscript: Kurniawan, N. A., Enemark, S., and Rajagopalan, R. The role of structure in the nonlinear mechanics of semiflexible polymer networks. (submitted) Kurniawan, N. A., Wong, L. H, and Rajagopalan, R. Early stiffening and softening of collagen: interplay of deformation mechanisms in biopolymer networks. (submitted) Manuscripts in preparation: Kurniawan, N. A., Wong, L. H., Sun, W., Lim, C. T., Too, H.-P., and Rajagopalan, R. Strain-dependent viscoelasticity of collagen networks. (in preparation) iv Table of Contents Acknowledgments i Publications iv Table of Contents .v Summary .x List of Tables xii List of Figures . xiii List of Symbols . xvi Chapter : Introduction .1 1.1 Soft matter 1.2 Scale-dependent mechanics of soft matter .3 1.3 Characterization techniques of soft matter .5 1.3.1 Microscopy 1.3.2 Rheology .7 1.3.3 Scattering and spectroscopy techniques 1.3.4 Computer simulations .10 1.4 Scope and Structure of the Thesis 11 Chapter : Macromechanics of Collagen Networks 13 2.1 Introduction 13 2.1.1 Collagen 13 v 2.1.2 Bulk characterization of collagen networks 14 2.2 Materials and Methods .16 2.2.1 Collagen hydrogel preparation 16 2.2.2 Confocal reflection microscopy 17 2.2.3 Mechanical rheology .18 2.3 Results and Discussion .18 2.3.1 Collagen network microstructure 18 2.3.2 Rheology of collagen networks .21 2.3.3 Amplitude-dependent oscillatory shear measurement 26 2.3.4 Strain-dependent mechanics of collagen networks .31 2.3.5 Mechanics of collagen network rearrangements .37 2.4 Summary 42 Chapter : Mechanics of Semiflexible Polymer Networks 43 3.1 Introduction 43 3.2 Methods 46 3.2.1 Network model 46 3.2.2 Network generation and deformation 49 3.3 Results and Discussion .51 3.3.1 Network structural parameters 52 3.3.2 Length-scale-dependent network mechanics at small strain .54 3.3.3 Nonlinear strain-dependent network mechanics .56 3.3.4 Network deformation mechanism .59 vi 3.4 Conclusions 61 Chapter : Microrheology of Collagen Networks 63 4.1 Introduction 63 4.2 Microrheology 64 4.3 Materials and Methods .68 4.3.1 Collagen hydrogel preparation with embedded beads 68 4.3.2 Imaging .69 4.3.3 Probe tracking .69 4.3.4 Extraction of microrheological information 71 4.4 Results and Discussion .71 4.4.1 Discrepancy with mechanical rheology results .71 4.4.2 Matrix heterogeneity .74 4.5 Discussion 78 Chapter : Image Correlation Spectroscopy for Microrheology 81 5.1 Introduction 81 5.1.1 Problems with current microrheological techniques .81 5.1.2 Image correlation spectroscopy .81 5.2 Materials and Methods .86 5.2.1 Sample preparation 86 5.2.2 Mechanical rheometry .87 5.2.3 Imaging .88 5.2.4 Data collection and analysis: ICS .88 vii 5.2.5 Extraction of microrheological information: ICS-µR .90 5.3 Results 91 5.3.1 Extraction of MSD from image correlation data .92 5.3.2 ICS-µR for Newtonian fluids 96 5.3.3 ICS-µR for viscoelastic networks .98 5.4 Discussion 101 Chapter : Probe-independent Image Correlation Spectroscopy 105 6.1 Introduction 105 6.2 Theory 106 6.2.1 Conventional ICS for point emitters .107 6.2.2 Probe-independent ICS .108 6.3 Materials and Methods .110 6.3.1 Computer simulations .110 6.3.2 Sample preparation and imaging .112 6.3.3 ICS analysis .113 6.4 Results 115 6.4.1 Probe-independent ICS on simulated images .115 6.4.2 Probe-independent ICS on confocal images .124 6.5 Discussion 127 Chapter : Conclusions and Outlook 130 7.1 Summary 130 7.2 Future Directions 134 viii Bibliography [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] 97:2051-2060. 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Tech. 72:323-332. 153 Appendix A: Steps in ICS-µR Appendix A: Steps in ICS-µR Here, we present the details of the practical aspects and implementations in the ICS-µR analysis. To help the reader with the various quantities involved in the analysis, Figure A illustrates the calculation stages that will be subsequently discussed. Figure A 1: A schematic overview of data analysis steps involved in ICS-µR. The steps A through F are explained in the text below. Steps A, B, and G are routinely followed in standard ICS measurements, whereas Steps D and F are routinely used in standard microrheology measurements. In the present work, we introduce Step C, which allows microrheological analysis from ICS data, as well as Step E, which improves the quality of the microrheological results extracted from the data. All symbols and their meanings in this Appendix are the same as those used in the main body of the thesis, and explanations of the notations are, therefore, not repeated unless necessary. 154 Appendix A: Steps in ICS-µR Step A The raw data obtained in ICS is a sequence of images which represent the image intensity i ( x, y, t ) in space (i.e., x and y ) and time t . The normalized intensity correlation function is calculated as a function of the spatial lag, ξ and η , as well as lag time, τ , using Eqs. (5.4) and (5.5). To minimize computation time, r (ξ ,η ,τ ) is calculated using the Fourier method [162]. Step B For each time lag τ , the spatial correlation function is taken to be a 2D Gaussian [Eq. (5.6)], as described in Section 5.2.4. This spatial fitting is typically done in the least square manner and only for the central correlation area (small ξ and η ) with zero weighting for the central point (i.e., ξ = η = ), where there is white noise contribution. We found that the optimum fit is obtained by including data points where ξ and η are smaller than 5–6 times the Gaussian width d . The output of this step is g (τ ) . Step C For 3D Gaussian intensity profile of the excitation volume, the functional form of the temporal correlation function for a system with 3D diffusion is [185] ⎛ τ g (τ ) = g ⎜1 + ⎜ τ D , xy ⎝ ⎞ ⎟⎟ ⎠ −1 ⎛ d z2 τ ⎞ ⎜⎜ + ⎟⎟ ⎝ d xy τ D , z ⎠ −1 , (A.1) where the translational diffusion relaxation times, τ D , in the lateral and axial directions are related to the diffusion coefficient , D , respectively, by 155 Appendix A: Steps in ICS-µR τ D , xy = ωxy2 D and τ D , z = ωz2 D . Equation (A.1) can thus be rewritten as ⎛ Dτ g (τ ) = g ⎜1 + ⎜ d xy ⎝ −1 ⎞ ⎛ Dτ ⎞ ⎟⎟ ⎜1 + ⎟ dz ⎠ ⎠ ⎝ −1 . (A.2) If one assumes that the local effective D can be related to the MSD of the probe particles, ∆r (τ ) , by ∆r (τ ) = Dτ , then Eq. (A.2) becomes ⎛ ∆r (τ ) g (τ ) = g ⎜1 + ⎜ 3d xy2 ⎝ ⎞ ⎟ ⎟ ⎠ −1 ⎛ ∆r (τ ) ⎜1 + ⎜ 3d z2 ⎝ ⎞ ⎟ ⎟ ⎠ −1 . (A.3) Therefore, by solving (A.3), one can obtain the MSD data from the temporal correlation function. Step D The logarithmic derivative of ∆r (τ ) with respect to time is calculated as in Eq. (4.5). Numerical derivation in this process typically uses Gaussian sliding window approach [143], which inherently involve smoothing of the ∆r (τ ) data to reduce high-frequency noise in the data. This step is not needed for the method we propose (which requires only Steps E, which improves the quality of the extracted results). Step E One can, in principle, directly calculate G ' (ω ) and G " (ω ) from the ∆r (τ ) and α (τ ) data obtained in Steps C and D. However, the use of such an approach could lead to propagation of experimental and data processing errors arising from Step B and the Eqs. (A.3) and (4.5). In Step E here, we propose an alternative method that minimizes these errors. 156 Appendix A: Steps in ICS-µR Since g (τ ) , ∆r (τ ) , and α (τ ) are dependent on each other [as mathematically described in Eqs. (A.3) and (4.5)], we use an approach that eliminates the need for Eq. (4.5) and determines α (τ ) directly from g (τ ) by choosing a robust functional form for α (τ ) , writing ∆r (τ ) in terms of α (τ ) , and substituting in Eq. (A.3). We choose Eq. (5.8) to this and determine the parameters in Eq. (5.8) by a statistical analysis of the raw g (τ ) data (from Step B). The functional form in Eq. (5.8) has the advantage of being able to describe asymptotic power laws and the transitions, which are prevalent in many viscoelastic materials, as stated in Section 5.3.1. Step F The ∆r (τ ) and α (τ ) data obtained from Step E can then be used to calculate the frequency-dependent storage modulus, G ' (ω ) , and loss modulus, G " (ω ) , using Eqs. (4.6) and (4.7). Step G In addition to the microrheological information obtained in the previous steps, a number of ‘standard’ ICS measurements can also be obtained from the spatiotemporal correlation function r (ξ ,η ,τ ) . The methods to obtain this information can be found in the ICS literature, which has been extensively reviewed by Kolin and Wiseman [156]. 157 Appendix A: Steps in ICS-µR Illustrations To illustrate the usefulness of Step E, we show one typical extracted result based on this procedure and compare it to the result obtained from a combination of Steps C and D, for the raw g (τ ) data (Fig. S2), the ∆r (τ ) data (Fig. S3), as well as the G ' (ω ) and G " (ω ) data (Fig. S4). Finally, we compare the ICS-µR results for complex, viscoelastic materials (PEO solutions of different concentrations) with results obtained using mechanical rheology in Fig. S5. Note that as the material becomes increasingly liquid-like at low frequency, both the magnitude and quality of the G ' data decrease rapidly. For that reason and because of the logarithmic scale used in the y-axis, the error bar grows in size and the deviation between the results from the two methods may mistakenly seem to grow. Figure A 2: Comparison between the raw, unsmoothed g (τ ) data obtained from Step B and the extracted g (τ ) data obtained from Step E. The bottom panel shows the difference between the two data sets. 158 Appendix A: Steps in ICS-µR Figure A 3: Comparison between the ∆r (τ ) data obtained from Step C and the extracted ∆r (τ ) data obtained from Step E. Note the data truncation in the raw data at small τ due to amplified carry-over noise from the raw g (τ ) data in Step B. Figure A 4: Comparison between the ‘raw’ G ' (ω ) and G " (ω ) data obtained from Steps C, D, and F and the extracted G ' (ω ) and G " (ω ) data obtained from Steps E and F. The noise in the raw g (τ ) data (Figure A 2) is doubly amplified through calculation of ∆r (τ ) in Step C (Figure A 3) and α (τ ) in Step D, forcing severe data truncations in the ‘raw’ G ' (ω ) and G " (ω ) data. 159 Appendix A: Steps in ICS-µR Figure A 5: Comparison between frequency-dependent linear viscoelastic moduli for PEO aqueous solutions of various concentrations as measured with ICS-µR and mechanical rheometer (MR). ICS-µR results were obtained from ∆r (τ ) of 0.5 µm beads in the solutions. The error bars signify the extent of experimental error in the mechanical rheology measurement. 160 [...]... Introduction various other fields in soft matter research and beyond It is no wonder that de Gennes is now considered one of the founding fathers of soft matter [5] He succinctly summarize the two outstanding features of soft matter in his Nobel Lecture: its complexity and flexibility [6] Due to the various systems and applications that the term soft matter covers, the study of soft matter has become a highly... constants, but functions of time scale, length scale, and extent of deformation All of this scale-dependent behavior of soft matter systems calls for multiple characterization approaches 1.3 Characterization techniques of soft matter In this section, we briefly survey the various characterization techniques for studying the structure and properties of soft matter There are a large number of available techniques... advancement of soft matter research in the recent years, especially with the blossoming of nanotechnology and biophysics of biological materials There are a number of common features among soft matter systems that distinguish them as a class of materials [2] Chief among these are: The importance of the relation between structure and property at mesoscopic length scales A soft matter system often self-organizes... ξ 0 , η0 Location of Gaussian center z Spatial (axial) dimension xx Chapter 1: Introduction Chapter 1: Introduction 1.1 Soft matter Soft matter, as its name suggests, is a class of materials that can be easily deformed, as a result of their unusual structural, mechanical, and chemical behaviors The seemingly loose definition allows soft matter to encompass a wide range of systems of varying components,... branching and orientation of polymer [29] 9 Chapter 1: Introduction 1.3.4 Computer simulations The need for multiscale characterization of soft matter, together with the rapidly increasing power of computers, makes computer simulations a valuable tool in understanding soft matter Modeling of soft matter systems can be done at multiple levels, from atomistic, molecular modeling in Molecular and Brownian... interdisciplinary subject, taking in aspects of physics, chemistry, materials science, and in specific cases also of biochemistry as well as chemical and mechanical engineering [3] As a result, there are many directions from which one can approach soft matter systems This thesis presents our contribution to the link between structure and mechanical behavior of soft matter systems at different length and... structures Such small energy scale needed to deform the structures is one of the origins of the macroscopic compliance characteristic of soft matter systems As we shall discuss further, proper utilization of this information can in fact be useful in revealing the behavior of these materials in different length scales It is obvious that soft matter is characterized by complexity, both in structure and dynamics,...7.2.1 Characterization of evolving soft matter 134 7.2.2 The role of other structural variables on the mechanics of semiflexible polymer networks 135 7.2.3 Probe-material interaction 136 7.2.4 Probeless microrheology 138 Bibliography .141 Appendix A: Steps in ICS-µR 154 ix Summary This thesis presents a phenomenological study of the mechanics of soft. .. approach to study the mechanical behavior of soft matter The organization of this thesis is summarized in the next section 1.4 Scope and Structure of the Thesis In the first part of the thesis, we investigate the mechanical behavior of networks of collagen, the most abundant protein in mammals Collagen fibrils form complex hierarchical structures with a great variety of properties, and collagen networks... computational characterization technique has its own strengths and weaknesses, as well as ranges of applicability To study complex materials like soft matter, therefore, employing just one technique is often insufficient to completely understand the underlying principles of material behaviors For example, interpretation of mechanical rheology data is sometimes difficult without concurrent in situ characterization . Symbols xvi Chapter 1 : Introduction 1 1.1 Soft matter 1 1.2 Scale-dependent mechanics of soft matter 3 1.3 Characterization techniques of soft matter 5 1.3.1 Microscopy 5 1.3.2 Rheology. MULTISCALE MECHANICAL CHARACTERIZATION OF SOFT MATTER NICHOLAS AGUNG KURNIAWAN NATIONAL UNIVERSITY OF SINGAPORE 2011 MULTISCALE MECHANICAL CHARACTERIZATION. phenomenological study of the mechanics of soft matter systems, particularly polymer networks. Due to the length- and time-scale dependence of the mechanical properties of these networks, it